This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The underlying concepts are based on differential geometry and the theory of Lie groups in the mathematical aspect, and on gauge theory in the physical aspect. A great deal of effort has been directed toward making the description elementary, clear and concise, so that beginners will have easy access to the topics.

This textbook describes the fundamental "physical" aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids....

Describes the fundamental "physical" aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. This book also emphasizes the dynamical aspects of fluid motions, illustrating v

A guide to the geometrical theory of dynamical systems, fluid flows and certain integrable systems. It helps to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples.